Preheat the oven to 350°F (175°C). Line an 8-inch (20 cm) square baking dish with parchment paper, allowing the paper to overhang the sides a bit so that you can easily lift out the brownies.
Bring about 1 inch (2.5 cm) of water to a simmer in a small sauce pot. Set a large heatproof bowl over the pot (make sure the bottom of the bowl doesn’t touch the water). Place the butter and chocolate in the bowl and heat gently, stirring occasionally, until melted and well combined. Remove the bowl from the heat, taking care not to splash any water into the chocolate.
Add the sugar, vanilla, and eggs and whisk vigorously for several minutes until very smooth. Stir in the flour and salt. Using a rubber spatula, scrape the batter into the prepared pan and spread it evenly.
Bake until puffed and just barely set, 40 to 50 minutes, depending on how done you like your brownies. They will look slightly domed in the pan (and may have cracked across the top surface) and will feel set, not liquidy, when tapped lightly with your finger. A toothpick inserted into the center won’t come out clean; the brownies will still be gooey immediately after baking but will set a little further as they cool to room temperature. Let them cool in the pan, then remove them from the pan using the parchment paper, cut into squares, and serve.
Store leftover brownies, tightly wrapped, at room temperature for up to 3 days.
Maria Zizka is a cookbook writer and recipe developer who has collaborated with leading chefs, including Elisabeth Prueitt, Jessica Koslow, and Suzanne Goin. She has co-authored numerous award-winning cookbooks, most recently Tartine All Day, Everything I Want to Eat, and This Is Camino. Her first solo cookbook, THE NEWLYWED TABLE, will be published on April 2, 2019.